The cause of story branching is always the player's actions, which can fall into four categories:

Informed choices Alice the Cat Burglar must deliver a stolen artifact to either the Templars or the Pagans, knowing that supporting one faction will bar her from doing any more assignments for the other.

Uninformed choicesBob the Knight is asked about his favorite song. Depending on his answer, either The Horde will sack his hometown in the next chapter, or the king will send him overseas.

Earlier gameplay performanceIf Alice raised an alarm and made her presence known while stealing the artifact, its original owners will find her and throw her in a dungeon. Otherwise, the faction she didn't support earlier will send an assassin after her.

How can story branching manifest itself?

In the strictest sense, story branching must manifest in at least one of three ways (henceforth referred to as "significantly altering the story"):

Different level progression After she is thrown in a dungeon, Alice must find a way to escape—taking her gaolers' valuables with her. If chased by an assassin, she instead has to lure him to an abandoned house, trap him inside, and set it on fire. Neither the dungeon, nor the house levels are available in the respective other path.

Different objective progression Depending on whether Bob remained loyal to the Templars or ran over to the Pagans, his objective during the Final Battle will be to kill the Great Shaman or the Templar Grand Master, respectively. Although the battlefield remains essentially the same, his allies and enemies change.

Cosmetic branching Depending on his allegiance, Bob will wear the Templar crest on his shield or the Pagan hackle on his helmet in the battle against The Horde, but that's the only thing it affects.

Another grey area are hidden levels or objectives that are wedged in-between two mandatory ones under certain conditions. These differ both from mutually exclusive paths outlined above (in that you can only gain from tackling the optional level/objective) and from side quests (in that they will be Lost Forever if you choose to skip right to the next mandatory level, whereas side quests are usually available right up until the Point of No Return). The greyness comes from the fact that hidden levels don't haveto have anything todo with the story and the story itself remains ultimately linear.

Hidden level/objective On her mission to steal the artifact earlier, Alice spotted a large treasure trove but failed to solve the puzzle that unlocked it. Now an opportunity presents itself to infiltrate a caravan transporting the treasure and finish the job.

Can story branches converge again?

Yes, this is done in a lot of games simply to minimize the production costs. There are two approaches to story branch convergence:

River delta-like branching occurs in games where each one of multiple distinct endings can only be reached by a specific sequence of plot-relevant choices. Choosing the "wrong" path even once locks all later branching points necessary to reach the desired ending, so the story never converges again after the very first branching. This is most popular in Visual Novels, since text, backgrounds, and event CGs are cheap enough to produce for exclusive use in individual branches.

Braid-like branching does not require multiple endings, since the plot branches remain tightly interwoven and always converge at the same central points (events, levels, objectives, choices) in every playthrough. While the resulting story is ultimately linear, it has a lot of variations, which can affect other branches and the endings. This is most common in Role-Playing Games, because their devs can adjust existing levels to the player's story instead of designing new ones from scratch.

One of the reasons why cosmetic branching and hidden levels are a grey area is that they only lend themselves to braid-like branching and cannot be used for the river delta-like approach.

What is NOT story branching?

Following setups are not considered story branching, despite making a contribution to the overall story non-linearity:

Side Quests. Although side quests increase the openness of the game world, they do not, by definition, significantly alter the main quest's level/objective/choice progression: the player makes a short detour, grabs some quick XP and loot, and goes right back to the main quest exactly where it was left off. If a particular assignment does affect the main quest, it becomes more like a part of it than a proper side quest.

Multiple single-player campaigns in the same game (e.g. Another Side, Another Story) are just that, independent storylines with different beginnings, climaxes, endings, and even main characters, rather than the same but variable story.

The above does not mean that side quests and missions to collect plot coupons cannot contain internally branching paths, but if these are fully self-contained (don't affect other quests), they are non-linear but overall plot is not.

Please put subtrope examples directly to the respective subtrope pages. Here is how to tell them apart:

Multiple Endings is the very last Story Branching of the game, after which the story doesn't branch again and the branches no longer converge into a single plot. This is by far the most common form of story branching, since the devs don't have to worry about the consequences of the player's choices later in the game, only about the ending cutscene. Many, many games feature a perfectly linear story with a Last-Second Ending Choice for this reason.

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